The realization space is
  [1   1   0   0   1   1        0             x1 - 2         1             x1 - 1           2*x1 - 2]
  [1   0   1   0   1   0   x1 - 2   -x1^2 + 4*x1 - 4   -x1 + 2   -x1^2 + 4*x1 - 4   -x1^2 + 4*x1 - 4]
  [0   0   0   1   1   1      -x1          x1^2 - x1        x1          x1^2 - x1               x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (3*x1^6 - 20*x1^5 + 53*x1^4 - 70*x1^3 + 46*x1^2 - 12*x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1^2 - 2*x1 + 2, 2, x1 - 1, 2*x1^2 - 5*x1 + 4, 2*x1 - 3, x1^2 - 3*x1 + 3]